Note that there are two limit cases of the spatial dynamics where the final epidemic outcome will only depend on \(\Theta \) , and not on \(\mathrm {T_{inf}}\) :
The well-mixed (mean-field) case, where agents are continuously exchanging neighbors, and the static interaction network case (if agents are close enough to form a connected graph), where the neighbors remain fixed.
In both situations, the newly infected agents are continuously interacting with other agents that are potentially susceptible, so the duration \(\mathrm {T_{inf}}\)  of their infectious state will not affect the outcome.
Even in these limits, however, the contagion process before reaching this final outcome will also depend on \(\mathrm {T_{inf}}\)  and on the spatial dynamics of the system, which will affect its timescale [1]}, [2]}, [3]}.
In more realistic cases where the interactions are determined by complex temporal networks [4]} or spatiotemporal dynamics, as in the model considered here, both the epidemic outcome and the contagion process will generally depend on all parameters.
